Remark 2.2 We note that the algebraic stack \(\mathfrak {M}^{ev}(\mathcal {X},\tau )\)  is not particularly well behaved. In particular, it is not of finite type, and contains an infinite collection of log strata. This is typically resolved by replacing \(\mathfrak {M}^{ev}(\mathcal {X},\tau )\)  with the complement of all log strata whose closure does not intersect the image of \(\mathcal {M}(X,\tau )\) . The latter space is of finite type, as seen for instance by [1]} Theorem \(3.11\) . One of the essential ingredients missing from \(\mathfrak {M}^{ev}(\mathcal {X},\tau )\)  is the combinatorial restriction imposed by the logarithmic balancing condition, intersection numbers with components of the boundary divisor.

